10,774 research outputs found

    On the Parisi-Toulouse hypothesis for the spin glass phase in mean-field theory

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    We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function q(x)q(x) is computed at high orders in powers of τ=Tc−T\tau=T_c-T and HH. We find that none of the Parisi-Toulouse scaling hypotheses on the q(x)q(x) behavior strictly holds, although some of them are violated only at high orders. The series is resummed yielding results in the whole spin-glass phase which are compared with those from a numerical evaluation of the q(x)q(x). At the high order considered, the transition turns out to be third order on the Almeida-Thouless line, a result which is confirmed rigorously computing the expansion of the solution near the line at finite τ\tau. The transition becomes smoother for infinitesimally small field while it is third order at strictly zero field.Comment: 6 pages, 2 figure

    Physics of the linear collider

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    This presentation intends to illustrate the specific capabilities of an e+^+e−^- sub-TeV collider to provide answers on the basic issues in physics: origin of mass, hierarchy of masses, cosmological problems. Some foreseeable scenarios are discussed with a possible synergy with LHC.Comment: 20 pages, 16 figure
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